dorsal/arxiv
View SchemaA new view on relativity: Part 2. Relativistic dynamics
| Authors | Yaakov Friedman |
|---|---|
| Categories | |
| ArXiv ID | physics/0606009 |
| URL | https://arxiv.org/abs/physics/0606009 |
| DOI | 10.2478/v10005-007-0013-z |
| Journal | Concepts of Physics V.4 N. 2 (2007) 239-261 |
Abstract
The Lorentz transformations are represented on the ball of relativistically admissible velocities by Einstein velocity addition and rotations. This representation is by projective maps. The relativistic dynamic equation can be derived by introducing a new principle which is analogous to the Einstein's Equivalence Principle, but can be applied for any force. By this principle, the relativistic dynamic equation is defined by an element of the Lie algebra of the above representation. If we introduce a new dynamic variable, called symmetric velocity, the above representation becomes a representation by conformal, instead of projective maps. In this variable, the relativistic dynamic equation for systems with an invariant plane, becomes a non-linear analytic equation in one complex variable. We obtain explicit solutions for the motion of a charge in uniform, mutually perpendicular electric and magnetic fields. By the above principle, we show that the relativistic dynamic equation for the four-velocity leads to an analog of the electromagnetic tensor. This indicates that force in special relativity is described by a differential two-form.
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"abstract": "The Lorentz transformations are represented on the ball of relativistically\nadmissible velocities by Einstein velocity addition and rotations. This\nrepresentation is by projective maps. The relativistic dynamic equation can be\nderived by introducing a new principle which is analogous to the Einstein\u0027s\nEquivalence Principle, but can be applied for any force. By this principle, the\nrelativistic dynamic equation is defined by an element of the Lie algebra of\nthe above representation. If we introduce a new dynamic variable, called\nsymmetric velocity, the above representation becomes a representation by\nconformal, instead of projective maps. In this variable, the relativistic\ndynamic equation for systems with an invariant plane, becomes a non-linear\nanalytic equation in one complex variable. We obtain explicit solutions for the\nmotion of a charge in uniform, mutually perpendicular electric and magnetic\nfields. By the above principle, we show that the relativistic dynamic equation\nfor the four-velocity leads to an analog of the electromagnetic tensor. This\nindicates that force in special relativity is described by a differential\ntwo-form.",
"arxiv_id": "physics/0606009",
"authors": [
"Yaakov Friedman"
],
"categories": [
"physics.class-ph"
],
"doi": "10.2478/v10005-007-0013-z",
"journal_ref": "Concepts of Physics V.4 N. 2 (2007) 239-261",
"title": "A new view on relativity: Part 2. Relativistic dynamics",
"url": "https://arxiv.org/abs/physics/0606009"
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